The Characterization of Cheng's Multivariate Writhe Polynomial

Juno Park

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arXiv · 2608.26201

The Characterization of Cheng's Multivariate Writhe Polynomial

Juno Park

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Abstract

Cheng introduces the multivariate writhe polynomial, leaving a question regarding the characterization of this invariant. In this paper, we resolve this question by proving that a Laurent polynomial $f$ with integer coefficients can be realized as the multivariate writhe polynomial of some multi-virtual knot if and only if $f(1,\dots,1)=0$ and $\left. \frac{d}{dt} f(t, \dots, t) \right\vert{}_{t=1} = 0$.

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Juno Park. 2026-08-25. The Characterization of Cheng's Multivariate Writhe Polynomial. https://arxiv.org/abs/2608.26201

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